Acoustic reflectance measurements and their clinical applications have been the subject of many recent studies. These studies have shown that power reflectance, the magnitude squared of the complex acoustic reflectance (CAR), shows distinct and often systematic variations between pathological and normal middle ears (e.g. Feeney et al., 2003; Allen et al., 2005; Hunter et al., 2010). Studies by Voss et al. (2012) and Nakajima et al. (2012) have investigated the efficacy of reflectance measurements for differential diagnosis of middle ear pathology. Tympanometry and laser doppler vibrometry are the current standards for presurgical differentiation between ossicular fixation (Little to no movement of one or more of the three middle-ear bones), ossicular discontinuity (connection between 2 or more bones discontinues), and third window disorders (vibrations entering the ear canal and middle ear are then abnormally diverted through the superior semicircular canal and up into the intracranial space where they become absorbed instead of being registered as sound in the hearing center, the cochlea) (Rosowski et al., 2003). Tympanometry is an examination used to test the condition of the middle ear and mobility of the eardrum (tympanic membrane) and the conduction bones by creating variations of air pressure in the ear canal. Further, tympanometry is an objective test of middle-ear function. Tympanometry is not a hearing test, but rather a measure of energy transmission through the middle ear. Laser doppler vibrometry (LDV) is a scientific instrument that is used to make non-contact vibration measurements of a surface (e.g. an eardrum). The laser beam from the LDV is directed at the surface of interest, and the vibration amplitude and frequency are extracted from the Doppler shift of the reflected laser beam frequency due to the motion of the surface. Nakajima et al. concluded that analyzing the power reflectance performs as well as laser doppler vibrometry, both in combination with audiometry (e.g. airborne gap measurements), for differential diagnosis of middle ear disorders.
This is a valuable result, because CAR measurements can be performed using the United States Food and Drug Administration (FDA) 510(K) cleared HearID system (Mimosa Acoustics), which, as stated by Nakajima et al. (2012), costs an order of magnitude less than the laser Doppler vibrometer ($10; 000 vs. $100,000 USD) and requires less training to operate. In another recent study, Voss et al. (2012) systematically manipulated cadaver ears to isolate the effects of various pathologies with differing degrees of severity, and examined the CAR responses. They also concluded that power reflectance may be a strong supplement to audiometry for the diagnosis of certain pathologies of the middle ear.
CAR and impedance (where impedance is the inverse of admittance) are measured at ambient pressure by a probe (i.e. transducer) containing a microphone and loudspeaker, sealed in the ear canal via a foam tip. The probe is calibrated using a multi-cavity least squares procedure to find the Thévenin equivalent parameters of the acoustic source (as described in Allen, 1986). A stimulus (i.e. signal) is emitted by the probe, and the complex cavity pressure response is measured. From the calibration pressure responses, the acoustic impedance, reflectance, and related quantities (admittance, power reflectance, etc.) may be calculated. The CAR, denoted Γ(ω), is equal to the ratio of the reflected to incident wave pressure at the microphone, located in the ear canal, as a function of frequency (ω=2πf). The magnitude squared of the reflectance, |Γ(ω)|2, represents the relative acoustic power reflected back to the ear canal from the middle and inner ears (e.g. from the ear drum). The power reflectance is related to conductive hearing functionality and is therefore relevant to clinical assessment of the middle ear (Allen et al., 2005). The complex acoustic impedance Z(ω) and reflectance Γ(ω), as functions of frequency, are related byΓ(ω)=(Z(ω)/r0−1)/((Z(ω))/r0+1)  (1)
r0=ρc/A is the estimated surge resistance, ρ is the density of air, c is the speed of sound, and A is the area of the ear canal. The ‘surge’ impedance (Campbell) is defined as the amplitude of the δ(t) component of the time-domain impedance; because it is a real constant, it is denoted as a resistance. It follows that the reflectance is strictly causal (i.e. zero at t=0) (Claerbout, 1985).
The clinical utility of CAR depends on its capacity to discern normal from pathological results, which requires a method for comparing measurements across ears. Direct comparison of CAR is complicated because the residual ear canal dimensions between the probe tip and tympanic membrane (TM) vary across subjects. This uncertainty has a large effect on the reflectance phase and the complex acoustic impedance. The residual ear canal is frequently modeled as a rigid-walled tube of uniform area A and length L, having a volume A*L.
Under this assumption, the relationship between the CAR at the probe and at the TM becomesΓ(ω)=ΓTM(ω)e−(ρL/c)ω  (2)
In many cases this is not a realistic model, particularly because the residual ear canal area A(x) varies with distance x (Farmer-Fedor and Rabbitt, 2002). Equation (2) represents a special case of a uniform (constant A(x)), lossless canal; a nonuniform, lossless canal would have a more complicated phase dependence on frequency. However, consideration of the CAR magnitude (or the power reflectance |Γ(ω)|2) is highly effective because even when A(x) is nonuniform, the ear canal may be reasonably approximated as lossless, in which case|Γ(ω)|=|ΓTM(ω)|  (3)
Eliminating the variation due to the residual ear canal length (or volume) by using the CAR magnitude or power reflectance allows for comparison across measurements with unknown residual canal dimensions. Thus, the magnitude reflectance is the current diagnostic standard using CAR measurements. The relationship in Eq. (3) was experimentally verified by Voss et al. (2008).
While uncertainty in the residual ear canal length/volume significantly confounds phase information associated with the eardrum and ossicles, taking the magnitude of the CAR eliminates this relevant information entirely. It follows that a holistic analysis of the CAR data could be more powerful and generalizable if the canal effect were accounted for in a rigorous manner, without eliminating the phase data (YTM({acute over (ω)})). The pending disclosure describes such embodiments of systems, methods, and devices for concise parametric characterization of CAR measurements, thereby determining the effect of the residual ear canal on the CAR, the ear drum impedance with the ultimate goal of improving differential diagnosis of middle ear pathology. This is accomplished by fitting poles and zeros to the CAR data.
Accordingly, there is a need for systems, methods, and devices for characterizing ear canal acoustic impedance and reflectance by pole-zero fitting. The pending disclosure incorporates by reference “Characterizing the ear canal acoustic impedance and reflectance by pole-zero fitting” by Sarah R. Robinson, Cac T. Nguyen, and Jont B. Allen, Hearing Research 301 (2013) 168-182. The following reference are incorporated by reference in their entireties:
Aibara, R., Welsh, J. T., Puria, S., Goode, R. L., 2001. Human middle-ear sound transfer function and cochlear input impedance. Hearing Research 152, 100-109; Allen, J. B., 1986. Measurement of Eardrum Acoustic Impedance. In: Allen, J. B., Hall, J. L., Hubbard, A., Neely, S. T., Tubis, A. (Eds.), Peripheral Auditory Mechanisms. Springer-Verlag, New York, pp. 44-51; Allen, J. B., Jeng, P. S., Levitt, H., 2005. Evaluation of human middle ear function via an acoustic power assessment. Journal of Rehabilitation Research & Development 42, 63-78; Brune, O., 1931. Synthesis of a finite two-terminal network whose driving-point impedance is a prescribed function of frequency. Journal of Mathematical
Physics 10, 191-236; Campbell, G. A., 1922. Physical theory of the electric wave filter. Bell System Technical Journal 1, 1-32; Claerbout, J., 1985. Imaging the Earth's Interior. Blackwell Scientific, Palo Alto, Calif., pp. 287-289; Farmer-Fedor, B. L., Rabbitt, R. D., 2002. Acoustic intensity, impedance and reflection coefficient in the human ear canal. The Journal of the Acoustical Society of America 112, 600-620; Feeney, M. P., Grant, I. L., Marryott, L. P., 2003. Wideband energy reflectance measurements in adults with middle-ear disorders. Journal of Speech, Language, and Hearing Research 46, 901-911; Fletcher, H., 1925. Useful numerical constants of speech and hearing. Bell System Technical Journal IV, 375-386; Gustaysen, B., Semlyen, A., 1999. Rational approximation of frequency domain responses by vector fitting. IEEE Transactions on Power Delivery 14, 1052-1061; Hunter, L. L., Feeney, M. P., Lapsley Miller, J. A., Jeng, P. S., Bohning, S., 2010. Wideband reflectance in newborns: nonnative regions and relationship to hearing-screening results. Ear and Hearing 31, 599-610; Keefe, D. H., Ling, R., Bulen, J. C., 1992. Method to measure acoustic impedance and reflection coefficient. The Journal of the Acoustical Society of America 91, 470-485; Kringlebotn, M., 1988. Network model for the human middle ear. Scandinavian Audiology 17, 75-85; Lundberg, K. H., Miller, H. R., Trumper, R. L., 2007. Initial conditions, generalized functions, and the Laplace transform: troubles at the origin. IEEE Control Systems Magazine 27, 22-35; Nakajima, H. H., Pisano, D. V., Roosli, C., Hamade, M. A., Merchant, G. R., Mahfoud, L., Halpin, C. F., Rosowski, J. J., Merchant, S. N., 2012. Comparison of ear-canal reflectance and umbo velocity in patients with conductive hearing loss: a preliminary study. Ear and Hearing 33, 35-43; Parent, P., Allen, J. B., 2010. Time-domain “wave” model of the human tympanic membrane. Hearing Research 263, 152-167; Puria, S., Allen, J. B., 1998. Measurements and model of the cat middle ear: evidence of tympanic membrane acoustic delay. The Journal of the Acoustical Society of America 104, 3463-3481; Rasetshwane, D. M., Neely, S. T., Allen, J. B., Shera, C. A., 2012. Reflectance of acoustic horns and solution of the inverse problem. The Journal of the Acoustical Society of America 131, 1863-1873; Recio-Spinoso, A., Fan, Y., Ruggero, A., 2011. Basilar-membrane responses to broadband noise modeled using linear filters with rational transfer functions, IEEE Transactions on Biomedical Engineering 58, 1456-1465; Rosowski, J. J., Mehta, R. P., Merchant, S. N., 2003. Diagnostic utility of laser-doppler vibrometry in conductive hearing loss with normal tympanic membrane. Otology & Neurotology 24, 165-175; Rosowski, J. J., Nakajima, H. H., Hamade, M. A., Mahfoud, L., Merchant, G. R., Halpin, C. F., Merchant, S. N., 2012. Ear-canal reflectance, umbo velocity, and tympanometry in normal-hearing adults. Ear and Hearing 33, 19-34; Rosowski, J. J., Nakajima, H. H., Merchant, S. N., 2008. Clinical utility of laser-doppler vibrometer measurements in live normal and pathologic human ears. Ear and Hearing 29, 3-19; Scheperle, R. A., Neely, S. T., Kopun, J. G., Gorga, M. P., 2008. Influence of in situ, sound-level calibration on distortion-product otoacoustic emission variability. The Journal of the Acoustical Society of America 124, 288-300; Van Valkenburg, M. E., 1964. Modern Network Synthesis. John Weily & Sons, Inc., New York, N. Y.; Voss, S. E., Allen, J. B., 1994. Measurement of acoustic impedance and reflectance in the human ear canal. The Journal of the Acoustical Society of America 95, 372-384; Voss, S. E., Horton, N. J., Woodbury, R. R., Sheffield, K. N., 2008. Sources of variability in reflectance measurements on normal cadaver ears. Ear and Hearing 29, 651-665; Voss, S. E., Merchant, G. R., Horton, N. J., 2012. Effects of middle-ear disorders on power reflectance measured in cadaveric ear canals. Ear and Hearing 33, 195-208; Voss, S. E., Rosowski, J. J., Merchant, S. N., Peake, W. T., 2000. Acoustic responses of the human middle ear. Hearing Research 150, 43-69; Withnell, R. H., Jeng, P. S., Waldvogel, K., Morgenstein, K., Allen, J. B., 2009. An in situ calibration for hearing thresholds. The Journal of the Acoustical Society of America 125, 1605-1611; Zwislocki, J., 1962. Analysis of the middle-ear function. part I: input impedance. The Journal of the Acoustical Society of America 34, 1514-1523; Robinson, S. R., Nguyen, C. T., & Allen, J. B. (2013). Characterizing the ear canal acoustic impedance and reflectance by pole-zero fitting. Hearing Research, 301, 168-182.
Skilled artisans will appreciate that elements in the figures are illustrated for simplicity and clarity and have not necessarily been drawn to scale. For example, the dimensions of some of the elements in the figures may be exaggerated relative to other elements to help to improve understanding of embodiments of the present invention.
The apparatus and method components have been represented where appropriate by conventional symbols in the drawings, showing only those specific details that are pertinent to understanding the embodiments of the present invention so as not to obscure the disclosure with details that will be readily apparent to those of ordinary skill in the art having the benefit of the description herein.